Answer: 0.9765
Explanation:
The cumulative distribution function for exponential distribution for random variable x is given by :-
[tex]F(x)=1-e^{-\lambda x}[/tex], where [tex]\lambda[/tex] is the mean of the distribution .
Given : On average, 5 customers arrive at the drive-up window of a fast-food restaurant every 4 minutes during the lunch hour.
Then [tex]\lambda=\dfrac{5}{4}=1.25[/tex]
Now, the probability that the next customer will arrive within three minutes :-
[tex]P(x< 3)=1-e^{-1.25 \times 3}=0.97648225\approx0.9765[/tex]
Hence, the probability that the next customer will arrive within three minutes = 0.9765
